Middle School Math Moments (now Cognitive Cardio Math)

I just wanted to share a couple pictures of our super-cuddly Boston Terrier, Lily. She is the funniest dog, when it comes to getting cuddled up in blankets. She's seven years old, and for years, we'd find her buried under blankets in the morning, never quite sure how she'd get herself under them so well. We now know that she will paw at the blankets, pull them with her teeth, and move them around so that she can duck her head under the edge and then nudge her head under the blankets, farther and farther until she's well underneath. It's so funny to watch! She can be so persistent. In the first picture here, she had a pretty easy time of getting between the layers of blankets to cuddle up. In the second picture, she was just cuddled up next to my daughter, asleep, covered in her blankets, of course. We think she is just the cutest!

I like to do a lot of problem solving with my students, usually having them work together so that they can model for each other and share/listen to each others' thinking. For the past two days, most of my math classes have been working on "Party Planning," which is the problem pictured here.  Students worked with one or two partners, to come up with combinations of foods that "Reggie" could buy for a party. I love listening to the kids' conversations as they work on things like this - "No one eats pretzels," "I'd choose candy and chips over pretzels," and so on. The students had a few important questions for me, though, as they were pretty serious about this planning:  Is this a "regular" party or like a sleep-over party, because the kind of food would depend on how long the party is."  "How big is the container of ice cream?"  "How big is the bag of candy?" And then there were a few other ideas,...

We've been spending a bit of time on decimal operations. I have five math classes, and in four of the five, our work with decimal operations has gone pretty well. There are a few students who are still mixing up their rules - when to line the decimal point up and when not to. When to count the digits behind the decimal points and when not to. However, in the fifth math class, there are many students who are not "getting it," even though did work with decimal operations last year. Part of the not getting it, I believe, is due to the fact that they don't actually look at their answers and think about whether or not they make sense. For example, many students will take a problem like 18.9 - 8 and get 18.1 as the answer....and they don't notice that it doesn't make sense to take 8 from 18 and still have 18 left. We've had discussions, gone through so many examples, and they've practiced the operations individually (and did very well when adding and subtr...